The large $D$ membrane paradigm for general four-derivative theory of gravity with a cosmological constant

Abstract

We find the membrane equations which describe the leading order in $1/D$ dynamics of black holes in the $D\to \infty$ limit for the most general four-derivative theory of gravity in the presence of a cosmological constant. We work up to linear order in the parameter determining the strength of the four-derivative corrections to the gravity action and hence there are no ghost modes in the theory. We find that the effective membrane equations we obtain are the covariant version of the membrane equations in absence of the cosmological constant. We also find the world-volume stress tensor for the membrane whose conservation gives the membrane equations. We apply the membrane equations to predict the light quasi-normal mode spectrum of black holes and black branes in the theory of gravity under consideration.

arXiv commentTypos corrected, acknowledgement added

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Cited by in corpus (6)

• The Large D Limit of Einstein's Equations
• Equivalence of JT Gravity and Near-extremal Black Hole Dynamics in Higher Derivative Theory
• Large D membrane for Higher Derivative Gravity and Black Hole Second Law
• Black Rings in Large $D$ Membrane Paradigm at the First Order
• General Theory of Large D Membranes Consistent with Second Law of Thermodynamics
• Stress Tensor for Large-$D$ membrane at subleading orders